I'm going to go against what I just said re: don't apply human traits to otherworldy beings not meant to be comparable to human, lmao. I couldn't figure out what the cat (Daijin) wanted on my first watch, but it's a bit clearer on my second. He (randomly picked pronoun) really just wants to be with Suzume. When he tasted the meal she gave him, when he heard how she calls him, it's probably the first time he felt human love. And he wants that.
He doesn't understand that human love is earned and maintained. He thought just by being with her, she'll give her some more of that love. He took the easy way out of making someone else take his place.
(Which reminds me of how some people treat nature, taking the easy way out, not caring when disaster strikes, not caring what it'd do to others. But I think that's probably too far of a read into it)
When he lead Suzume around Japan, he didn't understand it was dangerous for the doors to be open (or even the concept of danger) didn't understand how people can be hurt, just that it's a thing that happens.
Haha look at me trying to psychoanalyze a being specifically meant to not be psychoanalyzed. Ah. I guess we really aren't capable of making characters that aren't also a bit like us.
On second watch, knowing that this is a story about making peace with disasters instead of the memories of abandoned places (which was my initial speculation), the prayer that Souta said when he closes door (and the voices that accompany it) just becomes infinitely sadder. Gods to whom these mountains and rivers belong and now we've called our own, we understand that we live side by side with death, and now we return this to you.
It's just... making peace with how your entire world can just be gone. The voices are memories of things that you'd thought routine, that you thought can keep on happening. Good morning! See you later!
But when disaster strikes there aren't any later. There aren't any more mornings. To accept it is to understand it.
I'm still crying as I think of that final door, before the tsunami hits, when people say to their loved ones that they're off to work and school, with the promise that they'll see each other again in the evening. There aren't any more evenings. They didn't see each other again.